#IT326 Project

Description of the dataset:

This dataset, obtained from vgchartz.com, provides a valuable resource for exploring the dynamics between gaming platforms and genres in the top 100 global video games. It enables us to analyze the platforms that are influencing worldwide sales, identify the most prosperous genres in various global regions, and track the evolving trends in both platform preference and genre popularity over time.

Our goal:

Our goal from studying this dataset is to utilize classification and clustering techniques on the input data to make predictions about the popularity of upcoming games.

Attributes description:

This dataset has 11 attributes and 16599 objects.

Rank: Ranking of the game based on global sales.

Name: Name of the game.

Platform: Platform the game was released on.

Year: Year the game was released.

Genre: Genre of the game.

Publisher: Publisher of the game.

NA_Sales: Sales of the game in North America.

EU_Sales: Sales of the game in Europe.

JP_Sales: Sales of the game in Japan.

Other_Sales: Sales of the game in other regions.

Global_Sales: Total sales of the game worldwide.

Class label:

Popular’ is our class label, we will use Global_Sales attribute to predict whether a game will sell 1000000 or more globally. Our task of data mining is regression.

dataset=read.csv("vgsales.csv")
Warning: cannot open file 'vgsales.csv': No such file or directoryError in file(file, "rt") : cannot open the connection

Importing our dataset.

library(outliers) 
library(dplyr)

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union
library(Hmisc)
Registered S3 methods overwritten by 'htmltools':
  method               from         
  print.html           tools:rstudio
  print.shiny.tag      tools:rstudio
  print.shiny.tag.list tools:rstudio
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

Attaching package: ‘Hmisc’

The following objects are masked from ‘package:dplyr’:

    src, summarize

The following objects are masked from ‘package:base’:

    format.pval, units
library(ggplot2)
library(cowplot)
library(mlbench)
library(caret)
Loading required package: lattice
library(faux)

************
Welcome to faux. For support and examples visit:
https://debruine.github.io/faux/
- Get and set global package options with: faux_options()
************
library(DataExplorer)
library(randomForest)
randomForest 4.7-1.1
Type rfNews() to see new features/changes/bug fixes.

Attaching package: ‘randomForest’

The following object is masked from ‘package:ggplot2’:

    margin

The following object is masked from ‘package:dplyr’:

    combine

The following object is masked from ‘package:outliers’:

    outlier

loading libraries needed for our data mining tasks.

nrow(dataset)
[1] 16598
ncol(dataset)
[1] 11
dim(dataset)
[1] 16598    11
names(dataset)
 [1] "Rank"         "Name"         "Platform"     "Year"         "Genre"       
 [6] "Publisher"    "NA_Sales"     "EU_Sales"     "JP_Sales"     "Other_Sales" 
[11] "Global_Sales"

General info about our dataset including number of rows and columns, and cheking dimensionality and coulumns names.

str(dataset)
'data.frame':   16598 obs. of  11 variables:
 $ Rank        : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Name        : chr  "Wii Sports" "Super Mario Bros." "Mario Kart Wii" "Wii Sports Resort" ...
 $ Platform    : chr  "Wii" "NES" "Wii" "Wii" ...
 $ Year        : chr  "2006" "1985" "2008" "2009" ...
 $ Genre       : chr  "Sports" "Platform" "Racing" "Sports" ...
 $ Publisher   : chr  "Nintendo" "Nintendo" "Nintendo" "Nintendo" ...
 $ NA_Sales    : num  41.5 29.1 15.8 15.8 11.3 ...
 $ EU_Sales    : num  29.02 3.58 12.88 11.01 8.89 ...
 $ JP_Sales    : num  3.77 6.81 3.79 3.28 10.22 ...
 $ Other_Sales : num  8.46 0.77 3.31 2.96 1 0.58 2.9 2.85 2.26 0.47 ...
 $ Global_Sales: num  82.7 40.2 35.8 33 31.4 ...

Dataset structure including number of coulums and rows, attribute types.

head(dataset, 10)

sample of raw dataset(first 10 rows).

tail(dataset, 10)

sample of raw dataset(last 10 rows).

summary(dataset)
      Rank           Name             Platform             Year              Genre          
 Min.   :    1   Length:16598       Length:16598       Length:16598       Length:16598      
 1st Qu.: 4151   Class :character   Class :character   Class :character   Class :character  
 Median : 8300   Mode  :character   Mode  :character   Mode  :character   Mode  :character  
 Mean   : 8301                                                                              
 3rd Qu.:12450                                                                              
 Max.   :16600                                                                              
  Publisher            NA_Sales          EU_Sales          JP_Sales       
 Length:16598       Min.   : 0.0000   Min.   : 0.0000   Min.   : 0.00000  
 Class :character   1st Qu.: 0.0000   1st Qu.: 0.0000   1st Qu.: 0.00000  
 Mode  :character   Median : 0.0800   Median : 0.0200   Median : 0.00000  
                    Mean   : 0.2647   Mean   : 0.1467   Mean   : 0.07778  
                    3rd Qu.: 0.2400   3rd Qu.: 0.1100   3rd Qu.: 0.04000  
                    Max.   :41.4900   Max.   :29.0200   Max.   :10.22000  
  Other_Sales        Global_Sales    
 Min.   : 0.00000   Min.   : 0.0100  
 1st Qu.: 0.00000   1st Qu.: 0.0600  
 Median : 0.01000   Median : 0.1700  
 Mean   : 0.04806   Mean   : 0.5374  
 3rd Qu.: 0.04000   3rd Qu.: 0.4700  
 Max.   :10.57000   Max.   :82.7400  

summary of our dataset.

var(dataset$NA_Sales)
[1] 0.6669712
var(dataset$EU_Sales)
[1] 0.2553799
var(dataset$JP_Sales)
[1] 0.0956607
var(dataset$Other_Sales)
[1] 0.03556559
var(dataset$Global_Sales)
[1] 2.418112

variance of numeric data

Graphs:

dataset2 <- dataset %>% sample_n(50)
tab <- dataset2$Platform %>% table()
precentages <- tab %>% prop.table() %>% round(3) * 100 
txt <- paste0(names(tab), '\n', precentages, '%') 

pie(tab, labels=txt , main = "Pie chart of Platform") 

We notice from the pie chart of platform attribute that releasing a game for PS users will increase the popularity of the game since it is the most common platform among gamers.

# coloring barplot and adding text
tab<-dataset$Genre %>% table() 

precentages<-tab %>% prop.table() %>% round(3)*100 

txt<-paste0(names(tab), '\n',precentages,'%') 

bb <- dataset$Genre %>% table() %>% barplot(axisnames=F, main = "Barplot for Popular genres ",ylab='count',col=c('pink','blue','lightblue','green','lightgreen','red','orange','red','grey','yellow','azure','olivedrab')) 

text(bb,tab/2,labels=txt,cex=1.5) 

In terms of genre, action games are the most popular, followed by sports and music games. It is safe to assume that a high number of genres of this nature exist due to their popularity and sales.

boxplot(dataset$NA_Sales , main="
BoxPlot for NA_Sales")

boxplot(dataset$EU_Sales, main="
 BoxPlot for EU_Sales")

boxplot(dataset$JP_Sales , main="
 BoxPlot for JP_Sales")

boxplot(dataset$Other_Sales , main="
 BoxPlot for Other_Sales") 

The boxplot of the Other-sales attribute indicate that the values are close to each other ,and there is a lot of outliers since the dataset represents the global sales of video games.

boxplot(dataset$Global_Sales , main="BoxPlot for Global_Sales")

The boxplot of the Global-sales attribute indicate that the values are close to each other ,and there is a lot of outliers since the dataset represents the global sales of video games.

qplot(data = dataset, x=Global_Sales,y=Genre,fill=I("yellow"),width=0.5 ,geom = "boxplot" , main = "BoxPlots for genre and Global_Sales")
Warning: `qplot()` was deprecated in ggplot2 3.4.0.

dataset$Year %>% table() %>% barplot( main = "Barplot for year")

pairs(~NA_Sales + EU_Sales + JP_Sales + Other_Sales + Global_Sales, data = dataset,
      main = "Sales Scatterplot")

We used Scatterplot to determine the type of correlation we have between the sales; we can see that the majority have positive correlation with each other.

Pre - processing

Varaible transformation

dataset$Rank=as.character(dataset$Rank)

Rank should be char and not numeric,because we will use them as ordinal data.

Null checking

sum(is.na(dataset$Rank))
[1] 0
NullRank<-dataset[dataset$Rank=="N/A",]
NullRank

checking for nulls in Rank (there is no nulls)

sum(is.na(dataset$Name))
NullName<-dataset[dataset$Name=="N/A",]
NullName

checking for nulls in name (there is no nulls)

sum(is.na(dataset$Platform))
[1] 0
NullPlatform<-dataset[dataset$Platform=="N/A",]

checking for nulls in Platform(there is no nulls)

sum(is.na(dataset$year))
[1] 0
NullYear<-dataset[dataset$Year=="N/A",]
NullYear

checking for nulls in year we won’t delete the null and we will leave them as global constant as it is because we want the sales data of them.

sum(is.na(dataset$Other_Sales))
[1] 0
NullOther_Sales<-dataset[dataset$Other_Sales=="N/A",]

There is no null values in the other_sales.

sum(is.na(dataset$Genre))
[1] 0
NullGenre<-dataset[dataset$Genre=="N/A",]
NullGenre

checking for nulls in Genre(there is no nulls)

sum(is.na(dataset$Publisher))
[1] 0
NullPublisher<-dataset[dataset$Publisher=="N/A",]
NullPublisher

checking for nulls in Publisher. we won’t delete the null and we will leave them as global constant as it is because we want the sales data of them.

sum(is.na(dataset$Global_Sales))
[1] 0
NullGlobal_Sales<-dataset[dataset$Global_Saless=="N/A",]

There is no null values in the Global_Sales.

Encoding

dataset$Platform=factor(dataset$Platform,levels=c("2600","3DO","3DS","DC","DS","GB","GBA","GC","GEN","GG","N64","NES","NG","PC","PCFX","PS","PS2","PS3","PS4","PSP","PSV","SAT","SCD","SNES","TG16","Wii","WiiU","WS","X360","XB","XOne"), labels=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31))

Since most machine learning algorithms work with numbers and not with text or categorical variables, this column will be encoded.

dataset$Genre=factor(dataset$Genre,levels=c("Action","Adventure","Fighting","Platform","Puzzle","Racing","Role-Playing","Shooter","Simulation","Sports","Strategy","Misc"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))

Since most machine learning algorithms work with numbers and not with text or categorical variables, this column will be encoded.

Outliers

outlier of NA_Sales

OutNA_Sales = outlier(dataset$NA_Sales, logical =TRUE)
Error in if (nrow(x) != ncol(x)) stop("x must be a square matrix") : 
  argument is of length zero

outlier of EU_Sales

OutEU_Sales = outlier(dataset$EU_Sales, logical =TRUE)
Error in if (nrow(x) != ncol(x)) stop("x must be a square matrix") : 
  argument is of length zero

outlier of JP_Sales

OutJP_Sales = outlier(dataset$JP_Sales, logical =TRUE)
Error in if (nrow(x) != ncol(x)) stop("x must be a square matrix") : 
  argument is of length zero

outlier of other_sales

OutOS=outlier(dataset$Other_Sales, logical=TRUE)  
Error in if (nrow(x) != ncol(x)) stop("x must be a square matrix") : 
  argument is of length zero

outlier of Global_sales

OutGS=outlier(dataset$Global_Sales, logical=TRUE)  
Error in if (nrow(x) != ncol(x)) stop("x must be a square matrix") : 
  argument is of length zero

Remove outliers

dataset= dataset[-Find_outlier,]
Error: object 'Find_outlier' not found

Normalization

datsetWithoutNormalization<-dataset

dataset before normalization

normalize <- function(x) {return ((x - min(x)) / (max(x) - min(x)))}
dataset$NA_Sales<-normalize(datsetWithoutNormalization$NA_Sales)
dataset$EU_Sales<-normalize(datsetWithoutNormalization$EU_Sales)
dataset$JP_Sales<-normalize(datsetWithoutNormalization$JP_Sales)
dataset$Other_Sales<-normalize(datsetWithoutNormalization$Other_Sales)
dataset$Global_Sales<-normalize(datsetWithoutNormalization$Global_Sales)

min-max normalization we will use the min-max normalization; it’s better for visualization.

Feautre selection

Our class label (popular) refers to Global_Sales. Other sales regions will be evaluated based on their importance to (global_sales) column. and those that are less important will be deleted from the dataset. use roc_curve area as score

roc_imp <- filterVarImp(x = dataset[,7:10], y = dataset$Global_Sales)

sort the score in decreasing order

roc_imp <- data.frame(cbind(variable = rownames(roc_imp), score = roc_imp[,1]))
roc_imp$score <- as.double(roc_imp$score)
roc_imp[order(roc_imp$score,decreasing = TRUE),]

we will rmove the (JP_Sales) because it is of low importance to our class_label(Global_Sales)

dataset<- dataset[,-9]

#Dataset after pre-processing

---
output: html_notebook
---
#IT326 Project




# Description of the dataset:

This dataset, obtained from vgchartz.com, provides a valuable resource for exploring the dynamics between gaming platforms and genres in the top 100 global video games. It enables us to analyze the platforms that are influencing worldwide sales, identify the most prosperous genres in various global regions, and track the evolving trends in both platform preference and genre popularity over time. 

# Source and link:
Source: vgchartz.com

URL link: https://www.kaggle.com/datasets/gregorut/videogamesales

# Our goal:

Our goal  from studying this dataset is to utilize classification and clustering techniques on the input data to make predictions about the popularity of upcoming games.



# Attributes description:

This dataset has 11 attributes and 16599 objects.

Rank: Ranking of the game based on global sales. 

Name: Name of the game. 

Platform: Platform the game was released on.

Year: Year the game was released. 

Genre: Genre of the game.

Publisher: Publisher of the game. 

NA_Sales: Sales of the game in North America. 

EU_Sales: Sales of the game in Europe. 

JP_Sales: Sales of the game in Japan. 

Other_Sales: Sales of the game in other regions.

Global_Sales: Total sales of the game worldwide.


# Class label:

Popular' is our class label, we will use Global_Sales attribute to predict whether a game will sell 1000000 or more globally. Our task of data mining is regression.




```{r}
dataset=read.csv("vgsales.csv")
```
Importing our dataset.


```{r}
library(outliers) 
library(dplyr)
library(Hmisc)
library(ggplot2)
library(cowplot)
library(mlbench)
library(caret)
library(faux)
library(DataExplorer)
library(randomForest)
options(max.print=9999999)
```

loading libraries needed for our data mining tasks.


```{r}
nrow(dataset)
ncol(dataset)
dim(dataset)
names(dataset)
```
General info about our dataset including  number of rows and columns, and cheking dimensionality and coulumns names.

```{r}
str(dataset)
```
Dataset structure including number of coulums and rows, attribute types. 

```{r}
head(dataset, 10)
```
sample of raw dataset(first 10 rows).

```{r}
tail(dataset, 10)
```
sample of raw dataset(last 10 rows).

```{r}
summary(dataset)
```
summary of our dataset.

```{r}
var(dataset$NA_Sales)
var(dataset$EU_Sales)
var(dataset$JP_Sales)
var(dataset$Other_Sales)
var(dataset$Global_Sales)
```
variance of numeric data

# Graphs:

```{r}
dataset2 <- dataset %>% sample_n(50)
tab <- dataset2$Platform %>% table()
precentages <- tab %>% prop.table() %>% round(3) * 100 
txt <- paste0(names(tab), '\n', precentages, '%') 

pie(tab, labels=txt , main = "Pie chart of Platform") 

```

We notice from the pie chart of platform attribute that releasing a game for PS users will increase the popularity of the game since it is the most common platform among gamers. 





```{r}
# coloring barplot and adding text
tab<-dataset$Genre %>% table() 

precentages<-tab %>% prop.table() %>% round(3)*100 

txt<-paste0(names(tab), '\n',precentages,'%') 

bb <- dataset$Genre %>% table() %>% barplot(axisnames=F, main = "Barplot for Popular genres ",ylab='count',col=c('pink','blue','lightblue','green','lightgreen','red','orange','red','grey','yellow','azure','olivedrab')) 

text(bb,tab/2,labels=txt,cex=1.5) 
```
In terms of genre, action games are the most popular, followed by sports and music games. It is safe to assume that a high number of genres of this nature exist due to their popularity and sales.


```{r}
boxplot(dataset$NA_Sales , main="
BoxPlot for NA_Sales")
```

```{r}
boxplot(dataset$EU_Sales, main="
 BoxPlot for EU_Sales")
```

```{r}
boxplot(dataset$JP_Sales , main="
 BoxPlot for JP_Sales")
```




```{r}
boxplot(dataset$Other_Sales , main="
 BoxPlot for Other_Sales") 
```  

The boxplot of the Other-sales attribute indicate that the values are close to each other ,and there is a lot of outliers since the dataset represents the global sales of video games. 




```{r}
boxplot(dataset$Global_Sales , main="BoxPlot for Global_Sales")

```  
The boxplot of the Global-sales attribute indicate that the values are close to each other ,and there is a lot of outliers since the dataset represents the global sales of video games. 




```{r}
qplot(data = dataset, x=Global_Sales,y=Genre,fill=I("yellow"),width=0.5 ,geom = "boxplot" , main = "BoxPlots for genre and Global_Sales")
```

```{r}
dataset$Year %>% table() %>% barplot( main = "Barplot for year")
```

```{r}
pairs(~NA_Sales + EU_Sales + JP_Sales + Other_Sales + Global_Sales, data = dataset,
      main = "Sales Scatterplot")
```    
We used Scatterplot to determine the type of correlation we have between the sales; we can see that the majority have positive correlation with each other. 
 
 
      
# Pre - processing

# Varaible transformation
```{r}
dataset$Rank=as.character(dataset$Rank)
```
Rank should be char and not numeric,because we will use them as ordinal data.

# Null checking
```{r}
sum(is.na(dataset$Rank))
NullRank<-dataset[dataset$Rank=="N/A",]
NullRank
```
checking for nulls in Rank (there is no nulls)
```{r}
sum(is.na(dataset$Name))
NullName<-dataset[dataset$Name=="N/A",]
NullName
```

checking for nulls in name (there is no nulls)

```{r}
sum(is.na(dataset$Platform))
NullPlatform<-dataset[dataset$Platform=="N/A",]


```
checking for nulls in Platform(there is no nulls)

```{r}
sum(is.na(dataset$Year))
NullYear<-dataset[dataset$Year=="N/A",]
NullYear
```
checking for nulls in year
we won't delete the null and we will leave them as global constant as it is because we want the sales data of them.


```{r}
sum(is.na(dataset$Other_Sales))
NullOther_Sales<-dataset[dataset$Other_Sales=="N/A",]


```
There is no null values in the other_sales.

```{r}
sum(is.na(dataset$Genre))
NullGenre<-dataset[dataset$Genre=="N/A",]
NullGenre
```
checking for nulls in Genre(there is no nulls)
```{r}
sum(is.na(dataset$Publisher))
NullPublisher<-dataset[dataset$Publisher=="N/A",]
NullPublisher
```
checking for nulls in Publisher.
we won't delete the null and we will leave them as global constant as it is because we want the sales data of them.


```{r}
sum(is.na(dataset$Global_Sales))
NullGlobal_Sales<-dataset[dataset$Global_Saless=="N/A",]


```
There is no null values in the Global_Sales.

# Encoding
```{r}
dataset$Platform=factor(dataset$Platform,levels=c("2600","3DO","3DS","DC","DS","GB","GBA","GC","GEN","GG","N64","NES","NG","PC","PCFX","PS","PS2","PS3","PS4","PSP","PSV","SAT","SCD","SNES","TG16","Wii","WiiU","WS","X360","XB","XOne"), labels=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31))
```
Since most machine learning algorithms work with numbers and not with text or categorical variables, this column will be encoded.

```{r}
dataset$Genre=factor(dataset$Genre,levels=c("Action","Adventure","Fighting","Platform","Puzzle","Racing","Role-Playing","Shooter","Simulation","Sports","Strategy","Misc"),labels=c(1,2,3,4,5,6,7,8,9,10,11,12))
```
Since most machine learning algorithms work with numbers and not with text or categorical variables, this column will be encoded.


# Outliers
outlier of NA_Sales
```{r}
OutNA_Sales = outlier(dataset$NA_Sales, logical =TRUE)
sum(OutNA_Sales)
Find_outlier = which(OutNA_Sales ==TRUE, arr.ind = TRUE)
OutNA_Sales
Find_outlier
```
outlier of EU_Sales
```{r}
OutEU_Sales = outlier(dataset$EU_Sales, logical =TRUE)
sum(OutEU_Sales)
Find_outlier = which(OutEU_Sales ==TRUE, arr.ind = TRUE)
OutEU_Sales
Find_outlier
```
outlier of JP_Sales
```{r}
OutJP_Sales = outlier(dataset$JP_Sales, logical =TRUE)
sum(OutJP_Sales)
Find_outlier = which(OutJP_Sales ==TRUE, arr.ind = TRUE)
OutJP_Sales
Find_outlier
```

outlier of other_sales 
```{r}
OutOS=outlier(dataset$Other_Sales, logical=TRUE)  
sum(OutOS)  
Find_outlier=which(OutOS==TRUE, arr.ind=TRUE)  
OutOS 
Find_outlier 

```


outlier of Global_sales 

```{r}
OutGS=outlier(dataset$Global_Sales, logical=TRUE)  
sum(OutGS)  
Find_outlier=which(OutGS==TRUE, arr.ind=TRUE)  
OutGS 
Find_outlier 

```



# Remove outliers 
```{r}
dataset= dataset[-Find_outlier,]
```



# Normalization

```{r}
datsetWithoutNormalization<-dataset
```
dataset before normalization

```{r}
normalize <- function(x) {return ((x - min(x)) / (max(x) - min(x)))}
dataset$NA_Sales<-normalize(datsetWithoutNormalization$NA_Sales)
dataset$EU_Sales<-normalize(datsetWithoutNormalization$EU_Sales)
dataset$JP_Sales<-normalize(datsetWithoutNormalization$JP_Sales)
dataset$Other_Sales<-normalize(datsetWithoutNormalization$Other_Sales)
dataset$Global_Sales<-normalize(datsetWithoutNormalization$Global_Sales)
```
min-max normalization
we will use the min-max normalization; it's better for visualization.


# Feautre selection
Our class label (popular) refers to Global_Sales. Other sales regions will be evaluated based on their importance to (global_sales) column. and those that are less important will be deleted from the dataset.
use roc_curve area as score
```{r}
roc_imp <- filterVarImp(x = dataset[,7:10], y = dataset$Global_Sales)
```
sort the score in decreasing order
```{r}
roc_imp <- data.frame(cbind(variable = rownames(roc_imp), score = roc_imp[,1]))
roc_imp$score <- as.double(roc_imp$score)
roc_imp[order(roc_imp$score,decreasing = TRUE),]
```
we will rmove the (JP_Sales) because it is of low importance to our class_label(Global_Sales)
```{r}
dataset<- dataset[,-9]
```

#Dataset after pre-processing
```{r}
print(dataset)
```

